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root/radiance/ray/src/rt/ambcomp.c
Revision: 2.98
Committed: Thu Apr 24 01:43:58 2025 UTC (13 days, 17 hours ago) by greg
Content type: text/plain
Branch: MAIN
Changes since 2.97: +6 -3 lines
Log Message: 
perf: Removed ambient collision test for -aa 0, and set maximum threshold to 7°

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 greg 2.98 static const char RCSid[] = "$Id: ambcomp.c,v 2.97 2025/01/18 03:49:00 greg Exp $";
3 greg 1.1 #endif
4     /*
5     * Routines to compute "ambient" values using Monte Carlo
6 greg 2.9 *
7 greg 2.27 * Hessian calculations based on "Practical Hessian-Based Error Control
8     * for Irradiance Caching" by Schwarzhaupt, Wann Jensen, & Jarosz
9     * from ACM SIGGRAPH Asia 2012 conference proceedings.
10     *
11 greg 2.46 * Added book-keeping optimization to avoid calculations that would
12     * cancel due to traversal both directions on edges that are adjacent
13     * to same-valued triangles. This cuts about half of Hessian math.
14     *
15 greg 2.9 * Declarations of external symbols in ambient.h
16     */
17    
18 greg 2.10 #include "copyright.h"
19 greg 1.1
20     #include "ray.h"
21 greg 2.25 #include "ambient.h"
22     #include "random.h"
23 greg 1.1
24 greg 2.86 #ifndef MINADIV
25     #define MINADIV 7 /* minimum # divisions in each dimension */
26     #endif
27    
28 greg 2.26 typedef struct {
29 greg 2.90 FVECT p; /* intersection point */
30 greg 2.83 float d; /* reciprocal distance */
31 greg 2.90 SCOLOR v; /* hemisphere sample value */
32 greg 2.44 } AMBSAMP; /* sample value */
33    
34     typedef struct {
35 greg 2.26 RAY *rp; /* originating ray sample */
36     int ns; /* number of samples per axis */
37 greg 2.61 int sampOK; /* acquired full sample set? */
38 greg 2.92 int atyp; /* RAMBIENT or TAMBIENT */
39 greg 2.90 SCOLOR acoef; /* division contribution coefficient */
40     SCOLOR acol; /* accumulated color */
41 greg 2.92 FVECT onrm; /* oriented unperturbed surface normal */
42 greg 2.61 FVECT ux, uy; /* tangent axis unit vectors */
43 greg 2.44 AMBSAMP sa[1]; /* sample array (extends struct) */
44 greg 2.26 } AMBHEMI; /* ambient sample hemisphere */
45    
46 greg 2.56 #define AI(h,i,j) ((i)*(h)->ns + (j))
47     #define ambsam(h,i,j) (h)->sa[AI(h,i,j)]
48 greg 2.26
49 greg 2.27 typedef struct {
50 greg 2.35 FVECT r_i, r_i1, e_i, rcp, rI2_eJ2;
51     double I1, I2;
52 greg 2.27 } FFTRI; /* vectors and coefficients for Hessian calculation */
53    
54 greg 2.26
55 greg 2.61 static int
56 greg 2.73 ambcollision( /* proposed direciton collides? */
57     AMBHEMI *hp,
58     int i,
59     int j,
60     FVECT dv
61     )
62     {
63 greg 2.74 double cos_thresh;
64     int ii, jj;
65 greg 2.75 /* min. spacing = 1/4th division */
66     cos_thresh = (PI/4.)/(double)hp->ns;
67 greg 2.98 if (cos_thresh > 7.*PI/180.) /* 7 degrees is enough in any case */
68     cos_thresh = 7.*PI/180.;
69 greg 2.74 cos_thresh = 1. - .5*cos_thresh*cos_thresh;
70     /* check existing neighbors */
71 greg 2.73 for (ii = i-1; ii <= i+1; ii++) {
72     if (ii < 0) continue;
73     if (ii >= hp->ns) break;
74     for (jj = j-1; jj <= j+1; jj++) {
75     AMBSAMP *ap;
76     FVECT avec;
77     double dprod;
78     if (jj < 0) continue;
79     if (jj >= hp->ns) break;
80     if ((ii==i) & (jj==j)) continue;
81     ap = &ambsam(hp,ii,jj);
82 greg 2.74 if (ap->d <= .5/FHUGE)
83     continue; /* no one home */
84 greg 2.73 VSUB(avec, ap->p, hp->rp->rop);
85     dprod = DOT(avec, dv);
86     if (dprod >= cos_thresh*VLEN(avec))
87     return(1); /* collision */
88     }
89     }
90 greg 2.74 return(0); /* nothing to worry about */
91 greg 2.73 }
92    
93    
94     static int
95 greg 2.61 ambsample( /* initial ambient division sample */
96     AMBHEMI *hp,
97     int i,
98     int j,
99     int n
100 greg 2.26 )
101     {
102 greg 2.61 AMBSAMP *ap = &ambsam(hp,i,j);
103     RAY ar;
104 greg 2.41 int hlist[3], ii;
105 greg 2.94 double ss[2];
106 greg 2.88 RREAL spt[2];
107     double zd;
108 greg 2.61 /* generate hemispherical sample */
109 greg 2.26 /* ambient coefficient for weight */
110     if (ambacc > FTINY)
111 greg 2.90 setscolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
112 greg 2.26 else
113 greg 2.90 copyscolor(ar.rcoef, hp->acoef);
114 greg 2.92 if (rayorigin(&ar, hp->atyp, hp->rp, ar.rcoef) < 0)
115 greg 2.41 return(0);
116 greg 2.26 if (ambacc > FTINY) {
117 greg 2.90 smultscolor(ar.rcoef, hp->acoef);
118     scalescolor(ar.rcoef, 1./AVGREFL);
119 greg 2.41 }
120     hlist[0] = hp->rp->rno;
121 greg 2.94 hlist[1] = AI(hp,i,j);
122     hlist[2] = samplendx;
123     multisamp(ss, 2, urand(ilhash(hlist,3)+n));
124 greg 2.73 resample:
125 greg 2.94 square2disk(spt, (j+ss[1])/hp->ns, (i+ss[0])/hp->ns);
126 greg 2.26 zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
127     for (ii = 3; ii--; )
128 greg 2.61 ar.rdir[ii] = spt[0]*hp->ux[ii] +
129 greg 2.26 spt[1]*hp->uy[ii] +
130 greg 2.92 zd*hp->onrm[ii];
131 greg 2.61 checknorm(ar.rdir);
132 greg 2.98 /* avoid coincident samples? */
133     if (!n & (ambacc > FTINY) & (hp->ns >= 4) &&
134     ambcollision(hp, i, j, ar.rdir)) {
135 greg 2.94 ss[0] = frandom(); ss[1] = frandom();
136 greg 2.75 goto resample; /* reject this sample */
137 greg 2.73 }
138 greg 2.56 dimlist[ndims++] = AI(hp,i,j) + 90171;
139 greg 2.61 rayvalue(&ar); /* evaluate ray */
140     ndims--;
141 greg 2.83 zd = raydistance(&ar);
142     if (zd <= FTINY)
143 greg 2.61 return(0); /* should never happen */
144 greg 2.90 smultscolor(ar.rcol, ar.rcoef); /* apply coefficient */
145 greg 2.83 if (zd*ap->d < 1.0) /* new/closer distance? */
146     ap->d = 1.0/zd;
147 greg 2.61 if (!n) { /* record first vertex & value */
148 greg 2.83 if (zd > 10.0*thescene.cusize + 1000.)
149     zd = 10.0*thescene.cusize + 1000.;
150     VSUM(ap->p, ar.rorg, ar.rdir, zd);
151 greg 2.90 copyscolor(ap->v, ar.rcol);
152 greg 2.61 } else { /* else update recorded value */
153 greg 2.90 sopscolor(hp->acol, -=, ap->v);
154 greg 2.61 zd = 1.0/(double)(n+1);
155 greg 2.90 scalescolor(ar.rcol, zd);
156 greg 2.61 zd *= (double)n;
157 greg 2.90 scalescolor(ap->v, zd);
158     saddscolor(ap->v, ar.rcol);
159 greg 2.61 }
160 greg 2.90 saddscolor(hp->acol, ap->v); /* add to our sum */
161 greg 2.41 return(1);
162     }
163    
164    
165 greg 2.82 /* Estimate variance based on ambient division differences */
166 greg 2.41 static float *
167     getambdiffs(AMBHEMI *hp)
168     {
169 greg 2.93 const double normf = 1./(pbright(hp->acoef) + FTINY);
170 greg 2.94 float *earr = (float *)calloc(2*hp->ns*hp->ns, sizeof(float));
171     float *ep;
172 greg 2.42 AMBSAMP *ap;
173 greg 2.81 double b, b1, d2;
174 greg 2.41 int i, j;
175    
176     if (earr == NULL) /* out of memory? */
177     return(NULL);
178 greg 2.81 /* sum squared neighbor diffs */
179 greg 2.95 ap = hp->sa;
180     ep = earr + hp->ns*hp->ns; /* original estimates to scratch */
181     for (i = 0; i < hp->ns; i++)
182 greg 2.42 for (j = 0; j < hp->ns; j++, ap++, ep++) {
183 greg 2.90 b = pbright(ap[0].v);
184 greg 2.41 if (i) { /* from above */
185 greg 2.90 b1 = pbright(ap[-hp->ns].v);
186 greg 2.82 d2 = b - b1;
187 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
188 greg 2.41 ep[0] += d2;
189     ep[-hp->ns] += d2;
190     }
191 greg 2.55 if (!j) continue;
192     /* from behind */
193 greg 2.90 b1 = pbright(ap[-1].v);
194 greg 2.82 d2 = b - b1;
195 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
196 greg 2.55 ep[0] += d2;
197     ep[-1] += d2;
198     if (!i) continue;
199     /* diagonal */
200 greg 2.90 b1 = pbright(ap[-hp->ns-1].v);
201 greg 2.82 d2 = b - b1;
202 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
203 greg 2.55 ep[0] += d2;
204     ep[-hp->ns-1] += d2;
205 greg 2.41 }
206     /* correct for number of neighbors */
207 greg 2.95 ep = earr + hp->ns*hp->ns;
208     ep[0] *= 6./3.;
209     ep[hp->ns-1] *= 6./3.;
210     ep[(hp->ns-1)*hp->ns] *= 6./3.;
211     ep[(hp->ns-1)*hp->ns + hp->ns-1] *= 6./3.;
212 greg 2.41 for (i = 1; i < hp->ns-1; i++) {
213 greg 2.95 ep[i*hp->ns] *= 6./5.;
214     ep[i*hp->ns + hp->ns-1] *= 6./5.;
215 greg 2.41 }
216     for (j = 1; j < hp->ns-1; j++) {
217 greg 2.95 ep[j] *= 6./5.;
218     ep[(hp->ns-1)*hp->ns + j] *= 6./5.;
219 greg 2.93 }
220 greg 2.95 /* blur final map to reduce bias */
221 greg 2.93 for (i = 0; i < hp->ns-1; i++) {
222 greg 2.94 float *ep2;
223 greg 2.93 ep = earr + i*hp->ns;
224 greg 2.94 ep2 = ep + hp->ns*hp->ns;
225     for (j = 0; j < hp->ns-1; j++, ep++, ep2++) {
226 greg 2.95 ep[0] += .5*ep2[0] + .125*(ep2[1] + ep2[hp->ns]);
227 greg 2.94 ep[1] += .125*ep2[0];
228     ep[hp->ns] += .125*ep2[0];
229 greg 2.93 }
230 greg 2.41 }
231     return(earr);
232     }
233    
234    
235 greg 2.43 /* Perform super-sampling on hemisphere (introduces bias) */
236 greg 2.41 static void
237 greg 2.61 ambsupersamp(AMBHEMI *hp, int cnt)
238 greg 2.41 {
239     float *earr = getambdiffs(hp);
240 greg 2.54 double e2rem = 0;
241 greg 2.41 float *ep;
242 greg 2.55 int i, j, n, nss;
243 greg 2.41
244     if (earr == NULL) /* just skip calc. if no memory */
245     return;
246 greg 2.54 /* accumulate estimated variances */
247 greg 2.55 for (ep = earr + hp->ns*hp->ns; ep > earr; )
248     e2rem += *--ep;
249 greg 2.41 ep = earr; /* perform super-sampling */
250 greg 2.81 for (i = 0; i < hp->ns; i++)
251     for (j = 0; j < hp->ns; j++) {
252 greg 2.55 if (e2rem <= FTINY)
253     goto done; /* nothing left to do */
254     nss = *ep/e2rem*cnt + frandom();
255 greg 2.62 for (n = 1; n <= nss && ambsample(hp,i,j,n); n++)
256 greg 2.77 if (!--cnt) goto done;
257 greg 2.61 e2rem -= *ep++; /* update remainder */
258 greg 2.41 }
259 greg 2.55 done:
260 greg 2.41 free(earr);
261     }
262    
263    
264 greg 2.61 static AMBHEMI *
265     samp_hemi( /* sample indirect hemisphere */
266 greg 2.90 SCOLOR rcol,
267 greg 2.61 RAY *r,
268     double wt
269     )
270     {
271 greg 2.92 int backside = (wt < 0);
272 greg 2.61 AMBHEMI *hp;
273     double d;
274     int n, i, j;
275 greg 2.77 /* insignificance check */
276 greg 2.90 d = sintens(rcol);
277     if (d <= FTINY)
278 greg 2.77 return(NULL);
279 greg 2.61 /* set number of divisions */
280 greg 2.92 if (backside) wt = -wt;
281 greg 2.61 if (ambacc <= FTINY &&
282 greg 2.94 wt > (d *= 0.8*r->rweight/(ambdiv*minweight + 1e-20)))
283 greg 2.61 wt = d; /* avoid ray termination */
284     n = sqrt(ambdiv * wt) + 0.5;
285 greg 2.86 i = 1 + (MINADIV-1)*(ambacc > FTINY);
286     if (n < i) /* use minimum number of samples? */
287 greg 2.61 n = i;
288     /* allocate sampling array */
289     hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
290     if (hp == NULL)
291     error(SYSTEM, "out of memory in samp_hemi");
292 greg 2.92
293     if (backside) {
294     hp->atyp = TAMBIENT;
295     hp->onrm[0] = -r->ron[0];
296     hp->onrm[1] = -r->ron[1];
297     hp->onrm[2] = -r->ron[2];
298     } else {
299     hp->atyp = RAMBIENT;
300     VCOPY(hp->onrm, r->ron);
301     }
302 greg 2.61 hp->rp = r;
303     hp->ns = n;
304 greg 2.90 scolorblack(hp->acol);
305 greg 2.62 memset(hp->sa, 0, sizeof(AMBSAMP)*n*n);
306 greg 2.61 hp->sampOK = 0;
307     /* assign coefficient */
308 greg 2.90 copyscolor(hp->acoef, rcol);
309 greg 2.61 d = 1.0/(n*n);
310 greg 2.90 scalescolor(hp->acoef, d);
311 greg 2.61 /* make tangent plane axes */
312 greg 2.92 if (!getperpendicular(hp->ux, hp->onrm, 1))
313 greg 2.61 error(CONSISTENCY, "bad ray direction in samp_hemi");
314 greg 2.92 VCROSS(hp->uy, hp->onrm, hp->ux);
315 greg 2.61 /* sample divisions */
316     for (i = hp->ns; i--; )
317     for (j = hp->ns; j--; )
318     hp->sampOK += ambsample(hp, i, j, 0);
319 greg 2.90 copyscolor(rcol, hp->acol);
320 greg 2.61 if (!hp->sampOK) { /* utter failure? */
321     free(hp);
322     return(NULL);
323     }
324     if (hp->sampOK < hp->ns*hp->ns) {
325     hp->sampOK *= -1; /* soft failure */
326     return(hp);
327     }
328 greg 2.86 if (hp->sampOK <= MINADIV*MINADIV)
329     return(hp); /* don't bother super-sampling */
330 greg 2.61 n = ambssamp*wt + 0.5;
331 greg 2.94 if (n >= 4*hp->ns) { /* perform super-sampling? */
332 greg 2.61 ambsupersamp(hp, n);
333 greg 2.90 copyscolor(rcol, hp->acol);
334 greg 2.61 }
335     return(hp); /* all is well */
336     }
337    
338    
339 greg 2.46 /* Return brightness of farthest ambient sample */
340     static double
341 greg 2.56 back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3)
342 greg 2.46 {
343 greg 2.56 if (hp->sa[n1].d <= hp->sa[n2].d) {
344     if (hp->sa[n1].d <= hp->sa[n3].d)
345 greg 2.90 return(hp->sa[n1].v[0]);
346     return(hp->sa[n3].v[0]);
347 greg 2.56 }
348     if (hp->sa[n2].d <= hp->sa[n3].d)
349 greg 2.90 return(hp->sa[n2].v[0]);
350     return(hp->sa[n3].v[0]);
351 greg 2.46 }
352    
353    
354 greg 2.27 /* Compute vectors and coefficients for Hessian/gradient calcs */
355     static void
356 greg 2.56 comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1)
357 greg 2.27 {
358 greg 2.56 double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
359     int ii;
360    
361     VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop);
362     VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop);
363     VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p);
364 greg 2.35 VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
365     rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
366 greg 2.27 dot_e = DOT(ftp->e_i,ftp->e_i);
367     dot_er = DOT(ftp->e_i, ftp->r_i);
368 greg 2.32 rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
369     rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
370     ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
371 greg 2.35 sqrt( rdot_cp );
372 greg 2.32 ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
373 greg 2.35 dot_e*ftp->I1 )*0.5*rdot_cp;
374 greg 2.32 J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
375 greg 2.46 for (ii = 3; ii--; )
376     ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
377 greg 2.27 }
378    
379    
380 greg 2.28 /* Compose 3x3 matrix from two vectors */
381 greg 2.27 static void
382     compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
383     {
384     mat[0][0] = 2.0*va[0]*vb[0];
385     mat[1][1] = 2.0*va[1]*vb[1];
386     mat[2][2] = 2.0*va[2]*vb[2];
387     mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
388     mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
389     mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
390     }
391    
392    
393     /* Compute partial 3x3 Hessian matrix for edge */
394     static void
395     comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
396     {
397 greg 2.35 FVECT ncp;
398 greg 2.27 FVECT m1[3], m2[3], m3[3], m4[3];
399     double d1, d2, d3, d4;
400     double I3, J3, K3;
401     int i, j;
402     /* compute intermediate coefficients */
403     d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
404     d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
405     d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
406     d4 = DOT(ftp->e_i, ftp->r_i);
407 greg 2.35 I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
408     / ( 4.0*DOT(ftp->rcp,ftp->rcp) );
409 greg 2.27 J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
410     K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
411     /* intermediate matrices */
412 greg 2.35 VCROSS(ncp, nrm, ftp->e_i);
413     compose_matrix(m1, ncp, ftp->rI2_eJ2);
414 greg 2.27 compose_matrix(m2, ftp->r_i, ftp->r_i);
415     compose_matrix(m3, ftp->e_i, ftp->e_i);
416     compose_matrix(m4, ftp->r_i, ftp->e_i);
417 greg 2.35 d1 = DOT(nrm, ftp->rcp);
418 greg 2.27 d2 = -d1*ftp->I2;
419     d1 *= 2.0;
420     for (i = 3; i--; ) /* final matrix sum */
421     for (j = 3; j--; ) {
422     hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
423     2.0*J3*m4[i][j] );
424     hess[i][j] += d2*(i==j);
425 greg 2.46 hess[i][j] *= -1.0/PI;
426 greg 2.27 }
427     }
428    
429    
430     /* Reverse hessian calculation result for edge in other direction */
431     static void
432     rev_hessian(FVECT hess[3])
433     {
434     int i;
435    
436     for (i = 3; i--; ) {
437     hess[i][0] = -hess[i][0];
438     hess[i][1] = -hess[i][1];
439     hess[i][2] = -hess[i][2];
440     }
441     }
442    
443    
444     /* Add to radiometric Hessian from the given triangle */
445     static void
446     add2hessian(FVECT hess[3], FVECT ehess1[3],
447 greg 2.46 FVECT ehess2[3], FVECT ehess3[3], double v)
448 greg 2.27 {
449     int i, j;
450    
451     for (i = 3; i--; )
452     for (j = 3; j--; )
453     hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
454     }
455    
456    
457     /* Compute partial displacement form factor gradient for edge */
458     static void
459     comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
460     {
461 greg 2.35 FVECT ncp;
462 greg 2.27 double f1;
463     int i;
464    
465 greg 2.35 f1 = 2.0*DOT(nrm, ftp->rcp);
466     VCROSS(ncp, nrm, ftp->e_i);
467 greg 2.27 for (i = 3; i--; )
468 greg 2.46 grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
469 greg 2.27 }
470    
471    
472     /* Reverse gradient calculation result for edge in other direction */
473     static void
474     rev_gradient(FVECT grad)
475     {
476     grad[0] = -grad[0];
477     grad[1] = -grad[1];
478     grad[2] = -grad[2];
479     }
480    
481    
482     /* Add to displacement gradient from the given triangle */
483     static void
484 greg 2.46 add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
485 greg 2.27 {
486     int i;
487    
488     for (i = 3; i--; )
489     grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
490     }
491    
492    
493     /* Compute anisotropic radii and eigenvector directions */
494 greg 2.53 static void
495 greg 2.27 eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
496     {
497     double hess2[2][2];
498     FVECT a, b;
499     double evalue[2], slope1, xmag1;
500     int i;
501     /* project Hessian to sample plane */
502     for (i = 3; i--; ) {
503     a[i] = DOT(hessian[i], uv[0]);
504     b[i] = DOT(hessian[i], uv[1]);
505     }
506     hess2[0][0] = DOT(uv[0], a);
507     hess2[0][1] = DOT(uv[0], b);
508     hess2[1][0] = DOT(uv[1], a);
509     hess2[1][1] = DOT(uv[1], b);
510 greg 2.38 /* compute eigenvalue(s) */
511     i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
512     hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
513     if (i == 1) /* double-root (circle) */
514     evalue[1] = evalue[0];
515     if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
516 greg 2.53 ((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
517     ra[0] = ra[1] = maxarad;
518     return;
519     }
520 greg 2.27 if (evalue[0] > evalue[1]) {
521 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[0]));
522     ra[1] = sqrt(sqrt(4.0/evalue[1]));
523 greg 2.27 slope1 = evalue[1];
524     } else {
525 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[1]));
526     ra[1] = sqrt(sqrt(4.0/evalue[0]));
527 greg 2.27 slope1 = evalue[0];
528     }
529     /* compute unit eigenvectors */
530     if (fabs(hess2[0][1]) <= FTINY)
531     return; /* uv OK as is */
532     slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
533     xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
534     for (i = 3; i--; ) {
535     b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
536     a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
537     }
538     VCOPY(uv[0], a);
539     VCOPY(uv[1], b);
540     }
541    
542    
543 greg 2.26 static void
544     ambHessian( /* anisotropic radii & pos. gradient */
545     AMBHEMI *hp,
546     FVECT uv[2], /* returned */
547 greg 2.28 float ra[2], /* returned (optional) */
548     float pg[2] /* returned (optional) */
549 greg 2.26 )
550     {
551 greg 2.27 static char memerrmsg[] = "out of memory in ambHessian()";
552     FVECT (*hessrow)[3] = NULL;
553     FVECT *gradrow = NULL;
554     FVECT hessian[3];
555     FVECT gradient;
556     FFTRI fftr;
557     int i, j;
558     /* be sure to assign unit vectors */
559     VCOPY(uv[0], hp->ux);
560     VCOPY(uv[1], hp->uy);
561     /* clock-wise vertex traversal from sample POV */
562     if (ra != NULL) { /* initialize Hessian row buffer */
563 greg 2.28 hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
564 greg 2.27 if (hessrow == NULL)
565     error(SYSTEM, memerrmsg);
566     memset(hessian, 0, sizeof(hessian));
567     } else if (pg == NULL) /* bogus call? */
568     return;
569     if (pg != NULL) { /* initialize form factor row buffer */
570 greg 2.28 gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
571 greg 2.27 if (gradrow == NULL)
572     error(SYSTEM, memerrmsg);
573     memset(gradient, 0, sizeof(gradient));
574     }
575     /* compute first row of edges */
576     for (j = 0; j < hp->ns-1; j++) {
577 greg 2.56 comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
578 greg 2.27 if (hessrow != NULL)
579 greg 2.92 comp_hessian(hessrow[j], &fftr, hp->onrm);
580 greg 2.27 if (gradrow != NULL)
581 greg 2.92 comp_gradient(gradrow[j], &fftr, hp->onrm);
582 greg 2.27 }
583     /* sum each row of triangles */
584     for (i = 0; i < hp->ns-1; i++) {
585     FVECT hesscol[3]; /* compute first vertical edge */
586     FVECT gradcol;
587 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
588 greg 2.27 if (hessrow != NULL)
589 greg 2.92 comp_hessian(hesscol, &fftr, hp->onrm);
590 greg 2.27 if (gradrow != NULL)
591 greg 2.92 comp_gradient(gradcol, &fftr, hp->onrm);
592 greg 2.27 for (j = 0; j < hp->ns-1; j++) {
593     FVECT hessdia[3]; /* compute triangle contributions */
594     FVECT graddia;
595 greg 2.46 double backg;
596 greg 2.56 backg = back_ambval(hp, AI(hp,i,j),
597     AI(hp,i,j+1), AI(hp,i+1,j));
598 greg 2.27 /* diagonal (inner) edge */
599 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
600 greg 2.27 if (hessrow != NULL) {
601 greg 2.92 comp_hessian(hessdia, &fftr, hp->onrm);
602 greg 2.27 rev_hessian(hesscol);
603     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
604     }
605 greg 2.39 if (gradrow != NULL) {
606 greg 2.92 comp_gradient(graddia, &fftr, hp->onrm);
607 greg 2.27 rev_gradient(gradcol);
608     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
609     }
610     /* initialize edge in next row */
611 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
612 greg 2.27 if (hessrow != NULL)
613 greg 2.92 comp_hessian(hessrow[j], &fftr, hp->onrm);
614 greg 2.27 if (gradrow != NULL)
615 greg 2.92 comp_gradient(gradrow[j], &fftr, hp->onrm);
616 greg 2.27 /* new column edge & paired triangle */
617 greg 2.56 backg = back_ambval(hp, AI(hp,i+1,j+1),
618     AI(hp,i+1,j), AI(hp,i,j+1));
619     comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
620 greg 2.27 if (hessrow != NULL) {
621 greg 2.92 comp_hessian(hesscol, &fftr, hp->onrm);
622 greg 2.27 rev_hessian(hessdia);
623     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
624     if (i < hp->ns-2)
625     rev_hessian(hessrow[j]);
626     }
627     if (gradrow != NULL) {
628 greg 2.92 comp_gradient(gradcol, &fftr, hp->onrm);
629 greg 2.27 rev_gradient(graddia);
630     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
631     if (i < hp->ns-2)
632     rev_gradient(gradrow[j]);
633     }
634     }
635     }
636     /* release row buffers */
637     if (hessrow != NULL) free(hessrow);
638     if (gradrow != NULL) free(gradrow);
639    
640     if (ra != NULL) /* extract eigenvectors & radii */
641     eigenvectors(uv, ra, hessian);
642 greg 2.32 if (pg != NULL) { /* tangential position gradient */
643     pg[0] = DOT(gradient, uv[0]);
644     pg[1] = DOT(gradient, uv[1]);
645 greg 2.27 }
646     }
647    
648    
649     /* Compute direction gradient from a hemispherical sampling */
650     static void
651     ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
652     {
653 greg 2.41 AMBSAMP *ap;
654     double dgsum[2];
655     int n;
656     FVECT vd;
657     double gfact;
658 greg 2.27
659 greg 2.29 dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */
660 greg 2.27 for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
661     /* use vector for azimuth + 90deg */
662     VSUB(vd, ap->p, hp->rp->rop);
663 greg 2.29 /* brightness over cosine factor */
664 greg 2.92 gfact = ap->v[0] / DOT(hp->onrm, vd);
665 greg 2.40 /* sine = proj_radius/vd_length */
666     dgsum[0] -= DOT(uv[1], vd) * gfact;
667     dgsum[1] += DOT(uv[0], vd) * gfact;
668 greg 2.26 }
669 greg 2.29 dg[0] = dgsum[0] / (hp->ns*hp->ns);
670     dg[1] = dgsum[1] / (hp->ns*hp->ns);
671 greg 2.26 }
672    
673 greg 2.27
674 greg 2.49 /* Compute potential light leak direction flags for cache value */
675     static uint32
676     ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
677 greg 2.47 {
678 greg 2.50 const double max_d = 1.0/(minarad*ambacc + 0.001);
679 greg 2.66 const double ang_res = 0.5*PI/hp->ns;
680     const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01);
681 greg 2.51 double avg_d = 0;
682 greg 2.50 uint32 flgs = 0;
683 greg 2.58 FVECT vec;
684 greg 2.62 double u, v;
685 greg 2.58 double ang, a1;
686 greg 2.50 int i, j;
687 greg 2.52 /* don't bother for a few samples */
688 greg 2.72 if (hp->ns < 8)
689 greg 2.52 return(0);
690     /* check distances overhead */
691 greg 2.51 for (i = hp->ns*3/4; i-- > hp->ns>>2; )
692     for (j = hp->ns*3/4; j-- > hp->ns>>2; )
693     avg_d += ambsam(hp,i,j).d;
694     avg_d *= 4.0/(hp->ns*hp->ns);
695 greg 2.52 if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */
696     return(0);
697     if (avg_d >= max_d) /* insurance */
698 greg 2.51 return(0);
699     /* else circle around perimeter */
700 greg 2.47 for (i = 0; i < hp->ns; i++)
701     for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
702     AMBSAMP *ap = &ambsam(hp,i,j);
703 greg 2.50 if ((ap->d <= FTINY) | (ap->d >= max_d))
704     continue; /* too far or too near */
705 greg 2.47 VSUB(vec, ap->p, hp->rp->rop);
706 greg 2.62 u = DOT(vec, uv[0]);
707     v = DOT(vec, uv[1]);
708     if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v)
709 greg 2.49 continue; /* occluder outside ellipse */
710     ang = atan2a(v, u); /* else set direction flags */
711 greg 2.66 for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step)
712 greg 2.50 flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
713 greg 2.47 }
714 greg 2.49 return(flgs);
715 greg 2.47 }
716    
717    
718 greg 2.26 int
719     doambient( /* compute ambient component */
720 greg 2.90 SCOLOR rcol, /* input/output color */
721 greg 2.26 RAY *r,
722 greg 2.92 double wt, /* negative for back side */
723 greg 2.27 FVECT uv[2], /* returned (optional) */
724     float ra[2], /* returned (optional) */
725     float pg[2], /* returned (optional) */
726 greg 2.49 float dg[2], /* returned (optional) */
727     uint32 *crlp /* returned (optional) */
728 greg 2.26 )
729     {
730 greg 2.61 AMBHEMI *hp = samp_hemi(rcol, r, wt);
731 greg 2.41 FVECT my_uv[2];
732 greg 2.61 double d, K;
733 greg 2.41 AMBSAMP *ap;
734 greg 2.61 int i;
735     /* clear return values */
736 greg 2.26 if (uv != NULL)
737     memset(uv, 0, sizeof(FVECT)*2);
738     if (ra != NULL)
739     ra[0] = ra[1] = 0.0;
740     if (pg != NULL)
741     pg[0] = pg[1] = 0.0;
742     if (dg != NULL)
743     dg[0] = dg[1] = 0.0;
744 greg 2.49 if (crlp != NULL)
745     *crlp = 0;
746 greg 2.61 if (hp == NULL) /* sampling falure? */
747     return(0);
748    
749     if ((ra == NULL) & (pg == NULL) & (dg == NULL) ||
750 greg 2.86 (hp->sampOK < 0) | (hp->ns < MINADIV)) {
751 greg 2.61 free(hp); /* Hessian not requested/possible */
752     return(-1); /* value-only return value */
753 greg 2.26 }
754 greg 2.91 if ((d = scolor_mean(rcol)) > FTINY) {
755     d = 0.99*(hp->ns*hp->ns)/d; /* normalize avg. values */
756 greg 2.38 K = 0.01;
757 greg 2.45 } else { /* or fall back on geometric Hessian */
758 greg 2.38 K = 1.0;
759     pg = NULL;
760     dg = NULL;
761 greg 2.53 crlp = NULL;
762 greg 2.38 }
763 greg 2.90 ap = hp->sa; /* single channel from here on... */
764 greg 2.26 for (i = hp->ns*hp->ns; i--; ap++)
765 greg 2.90 ap->v[0] = scolor_mean(ap->v)*d + K;
766 greg 2.26
767     if (uv == NULL) /* make sure we have axis pointers */
768     uv = my_uv;
769     /* compute radii & pos. gradient */
770     ambHessian(hp, uv, ra, pg);
771 greg 2.29
772 greg 2.26 if (dg != NULL) /* compute direction gradient */
773     ambdirgrad(hp, uv, dg);
774 greg 2.29
775 greg 2.28 if (ra != NULL) { /* scale/clamp radii */
776 greg 2.35 if (pg != NULL) {
777     if (ra[0]*(d = fabs(pg[0])) > 1.0)
778     ra[0] = 1.0/d;
779     if (ra[1]*(d = fabs(pg[1])) > 1.0)
780     ra[1] = 1.0/d;
781 greg 2.48 if (ra[0] > ra[1])
782     ra[0] = ra[1];
783 greg 2.35 }
784 greg 2.29 if (ra[0] < minarad) {
785     ra[0] = minarad;
786     if (ra[1] < minarad)
787     ra[1] = minarad;
788     }
789 greg 2.92 ra[0] *= d = 1.0/sqrt(fabs(wt));
790 greg 2.26 if ((ra[1] *= d) > 2.0*ra[0])
791     ra[1] = 2.0*ra[0];
792 greg 2.28 if (ra[1] > maxarad) {
793     ra[1] = maxarad;
794     if (ra[0] > maxarad)
795     ra[0] = maxarad;
796     }
797 greg 2.53 /* flag encroached directions */
798 greg 2.87 if (crlp != NULL) /* XXX doesn't update with changes to ambacc */
799 greg 2.49 *crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
800 greg 2.35 if (pg != NULL) { /* cap gradient if necessary */
801     d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
802     if (d > 1.0) {
803     d = 1.0/sqrt(d);
804     pg[0] *= d;
805     pg[1] *= d;
806     }
807     }
808 greg 2.26 }
809     free(hp); /* clean up and return */
810     return(1);
811     }